Basic properties
Modulus: | \(619\) | |
Conductor: | \(619\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(618\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 619.h
\(\chi_{619}(2,\cdot)\) \(\chi_{619}(10,\cdot)\) \(\chi_{619}(11,\cdot)\) \(\chi_{619}(12,\cdot)\) \(\chi_{619}(15,\cdot)\) \(\chi_{619}(18,\cdot)\) \(\chi_{619}(19,\cdot)\) \(\chi_{619}(21,\cdot)\) \(\chi_{619}(32,\cdot)\) \(\chi_{619}(40,\cdot)\) \(\chi_{619}(46,\cdot)\) \(\chi_{619}(48,\cdot)\) \(\chi_{619}(52,\cdot)\) \(\chi_{619}(55,\cdot)\) \(\chi_{619}(56,\cdot)\) \(\chi_{619}(59,\cdot)\) \(\chi_{619}(62,\cdot)\) \(\chi_{619}(65,\cdot)\) \(\chi_{619}(66,\cdot)\) \(\chi_{619}(67,\cdot)\) \(\chi_{619}(68,\cdot)\) \(\chi_{619}(69,\cdot)\) \(\chi_{619}(70,\cdot)\) \(\chi_{619}(75,\cdot)\) \(\chi_{619}(76,\cdot)\) \(\chi_{619}(78,\cdot)\) \(\chi_{619}(82,\cdot)\) \(\chi_{619}(83,\cdot)\) \(\chi_{619}(84,\cdot)\) \(\chi_{619}(85,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{309})$ |
Fixed field: | Number field defined by a degree 618 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{77}{618}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 619 }(12, a) \) | \(-1\) | \(1\) | \(e\left(\frac{77}{618}\right)\) | \(e\left(\frac{71}{206}\right)\) | \(e\left(\frac{77}{309}\right)\) | \(e\left(\frac{268}{309}\right)\) | \(e\left(\frac{145}{309}\right)\) | \(e\left(\frac{122}{309}\right)\) | \(e\left(\frac{77}{206}\right)\) | \(e\left(\frac{71}{103}\right)\) | \(e\left(\frac{613}{618}\right)\) | \(e\left(\frac{47}{618}\right)\) |